Theorem nfnaew

Description: All variables are effectively bound in a distinct variable specifier. Version of nfnae with a disjoint variable condition, which does not require ax-13 . (Contributed by Mario Carneiro, 11-Aug-2016) (Revised by Gino Giotto, 10-Jan-2024)

	Ref	Expression
Assertion	nfnaew	$$⊢Ⅎz\neg \forall xx=y$$

Proof

Step	Hyp	Ref	Expression
1		hbaev	$$⊢\forall xx=y\to \forall z\forall xx=y$$
2	1	nf5i	$$⊢Ⅎz\forall xx=y$$
3	2	nfn	$$⊢Ⅎz\neg \forall xx=y$$